To convert a decimal number to binary representation, we need to divide the decimal number successively by 2 until the quotient becomes zero. The remainders obtained in each division give us the binary digits of the number in reverse order.

Steps to find the number of bits needed for binary representation of a decimal number:

1. Divide the decimal number by 2 until the quotient becomes zero.
2. Count the number of remainders obtained in step 1.
3. Round up the number of bits to the nearest integer.

Example:
Let's consider the decimal number 1234.

1. Division by 2:
1234 / 2 = 617 remainder 0
617 / 2 = 308 remainder 1
308 / 2 = 154 remainder 0
154 / 2 = 77 remainder 0
77 / 2 = 38 remainder 1
38 / 2 = 19 remainder 0
19 / 2 = 9 remainder 1
9 / 2 = 4 remainder 1
4 / 2 = 2 remainder 0
2 / 2 = 1 remainder 0
1 / 2 = 0 remainder 1

2. Number of remainders obtained = 10

3. Number of bits needed for binary representation = 10 bits (rounded up from 9.2877)

Now let's consider the decimal number with 25 digits. Since the number is very large, we cannot perform the division manually. However, we can use the following formula to estimate the number of bits:

Number of bits = ceil(log2(decimal number))

where ceil is the ceiling function, which rounds up the result to the nearest integer, and log2 is the logarithm base 2 function.

Using this formula, we get:

Number of bits = ceil(log2(10^25)) = ceil(83.044) = 83 bits (rounded up)

Therefore, the correct answer is option D - 83.